On sheaves of Abelian groups and universality

Abstract

Universal elements are one of the most essential parts in research fields, investigating if there exist (or not) universal elements in different classes of objects. For example, classes of spaces and frames have been studied under the prism of this universality property. In this paper, studying classes of sheaves of Abelian groups, we construct proper universal elements for these classes, giving a positive answer to the existence of such elements in these classes.

Keywords

• sheaves
• universal sheaves
• universal spaces
• containing spaces
• saturated classes of spaces